A tyre dismounting apparatus adapted to be installed on a motor vehicle comprises: a base configured to be fixed to the motor vehicle; a frame, hinged to the base and tiltable about a tilting axis between a rest position and a working position; a tilting actuator connected to the base and to the frame to move the frame relative to the base; a wheel-holder unit configured to receive a wheel and lock it in place and rotating about an axis of rotation to drive the wheel in rotation about the axis of rotation; a longitudinal actuator connected to the frame and configured to move the wheel-holder unit along a longitudinal axis having at least one component in a vertical direction, parallel to the direction of the weight force; a working unit connected to the frame and including a rod and a tool connected to the rod. The tyre dismounting apparatus comprises a transverse actuator connected to the working unit to move it translationally relative to the wheel-holder unit along a transverse axis parallel to the tilting axis of the frame.